The standard Poisson disorder problem revisited

A change in the arrival rate of a Poisson process sometimes necessitates immediate action. If the change time is unobservable, then the design of online change detection procedures becomes important and is known as the Poisson disorder problem. Formulated and partially solved by Davis [Banach Center Publ., 1 (1976) 65-72], the standard Poisson problem addresses the tradeoff between false alarms and detection delay costs in the most useful way for applications. In this paper we solve the standard problem completely and describe efficient numerical methods to calculate the policy parameters.